We propose a generalized relational expression (GRE),which unifies all dimensional uncertainty relations (URs) through dimensional analysis. Here we find a general expression for UR where the product of two or n dimensional noncommutative physical quantities (PQs) is equal to the power product of the reduced Planck constant h, gravitational constant G, speed of light in vacuum c , Boltzmann constant k and elementary charge e, and find that any dimensioned PQ has a corresponding Planck scale. Since the same dimensions, many PQs have the identical Planck scale. All Planck scales are divided into two categories, one is the basic Planck scale and derived Planck scale, the other is the Fermi-Planck scale, Bose-Planck scale and Other Planck scales. The corresponding Planck scale for any PQ is proven to be equal to the power product of Planck length, Planck time, Planck mass, Planck temperature, and elementary charge (or Planck charge). Find the GRE that the power product of noncommutative PQ is equal to the power product of corresponding Planck scale. Applying GRE, we also find the Big Bang UR for the temperature and volume of the Big Bang, and the Schwarzschild Black Hole (SBH) UR for the mass and volume of the SBH. Considering quantum effects, these URs suggest that there are no singularities in the Big Bang and SBH. We show that the GRE is generalized, interesting, and significant.